"Construct c=a+b by drawing and calculating the direction and magnitude of c. The direction should be measured from the +x-axis" how do you do this problem?

The question seems to be incomplete, so i will answer in a general way.

Ok, i guess that here we have two vectors:

a = (Ax, Ay) and b = (Bx, By).

Now we have that:

c = a + b = (Ax, Ay) + (Bx, By) =  (Ax + Bx, Ay + By).

Now, to calculate the magnitude of a vector (x, y) we have:

√(x^2 + y^2)

Then the magnitude of c will be:

IcI = √( (Ax + Bx)^2 + (Ay + By)^2)

And for the direction:

First, the direction is already defined by the vector c.

But a more exact (and easy to read) way is:

When we have a vector (x, y).

The angle between this vector and the x-axis is given by:

Tan(θ) = y/x.

Then in the case of c.

Tan(θ) = (Ay + By)/(Ax + Bx)

θ = ATan( (Ay + By)/(Ax + Bx) )

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step-by-step explanation: